Energy & Momentum of a Photon (CIE A Level Physics)

A photon has an energy of 1.78 eV. 

Convert this energy into joules.

Calculate the wavelength of this photon.

3.80 × 10¹⁸ of these photons are emitted from a laser every second.

Calculate the energy transferred by the laser every hour.

Calculate the total momentum of 5 of these photons. 

Scientists are designing a prototype spaceship, with a mass of 4.9 × 10⁶ kg.

Once it has left the solar system, it will come to rest relative to Earth. It will then be accelerated by 4 very powerful lasers, which will be aimed at 4 large sails on the spaceship.

Each laser emits photons with a wavelength of 2.50 × 10⁻¹² m.

Calculate the energy of a single photon.

Calculate the momentum of a single photon.

Each laser emits 7.5 × 10²⁵ photons per second. 

[1]

[2]

Calculate the speed of this spaceship after an hour of receiving this electromagnetic radiation.

A heated filament and anode are placed in a vacuum, as shown in Fig 1.1. The anode has a gap through which electrons can pass.

Fig 1.1

A potential difference of 15 V is applied across the filament and anode.

An electron is then emitted from the heated filament with a speed of 1.5 × 10⁶ m s⁻¹. 

Calculate its initial kinetic energy in electronvolts.

Calculate the electron's final kinetic energy in joules, as it exits the gap in the anode.

Calculate the momentum of this electron after it has passed through the hole in the anode. 

Calculate the number of 3.62 × 10¹⁴ Hz photons required to have an equivalent total momentum to the electron. Give your answer to two significant figures.

Photon energy and photon momentum are related by the equation:

E² = (pc)² + (mc²)²

Derive from this equation the equation  for calculating the momentum of a photon.

A photon has a wavelength of 400 nm. 

Calculate the velocity of an electron with the same momentum. 

Determine the ratio of photon energy to electron kinetic energy. 

A laser sitting at rest on wheels that are free to move produces 5.00 × 10²⁷ photons. Each photon has a frequency 3.95 × 10¹⁴ Hz. 

Calculate the magnitude of the momentum in producing these photons on the laser. 

Show that the equation used for part a) is homogeneous. 

Lasers produce photons of light through a process called stimulated emission. The energy of a photon produced by the laser is equal to the energy difference between the electrons in an excited state and the level below. Fig. 1.1 shows the energy levels of the electrons inside the laser from parts a) and b).

Fig. 1.1

Sketch on Fig. 1.1 the energy level transition of the electrons in the laser.